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UNIFORM DEFINABILITY IN PROPOSITIONAL DEPENDENCE LOGIC

Published online by Cambridge University Press:  12 January 2017

FAN YANG
FAN YANG*
Affiliation:
Department of Values, Technology and Innovation, Delft University of Technology
*
*DEPARTMENT OF VALUES, TECHNOLOGY AND INNOVATION DELFT UNIVERSITY OF TECHNOLOGY, JAFFALAAN 5 2628 BX DELFT, THE NETHERLANDS E-mail: [email protected]
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Abstract

Both propositional dependence logic and inquisitive logic are expressively complete. As a consequence, every formula in the language of inquisitive logic with intuitionistic disjunction or intuitionistic implication can be translated equivalently into a formula in the language of propositional dependence logic without these two connectives. We show that although such a (noncompositional) translation exists, neither intuitionistic disjunction nor intuitionistic implication is uniformly definable in propositional dependence logic.

Keywords

03B60dependence logicinquisitive logicuniform definabilitycompositionalityteam semantics
Type
Research Article
Information
The Review of Symbolic Logic , Volume 10 , Issue 1 , March 2017 , pp. 65 - 79
Copyright
Copyright © Association for Symbolic Logic 2017 

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Footnotes

This research was carried out in the Graduate School in Mathematics and its Applications of the University of Helsinki, Finland. Results of this paper were included in the dissertation (Yang, 2014) of the author.

References

BIBLIOGRAPHY

Ciardelli, I. (2009). Inquisitive Semantics and Intermediate Logics. Master’s Thesis, University of Amsterdam.Google Scholar
Ciardelli, I. & Roelofsen, F. (2011). Inquisitive logic. Journal of Philosophical Logic, 40(1), 55–94.Google Scholar
Galliani, P. (2013). Epistemic operators in dependence logic. Studia Logica, 101(2), 367–397.Google Scholar
Goranko, V. & Kuusisto, A. (2016). Logics for propositional determinacy and independence, arXiv:1609.07398.Google Scholar
Henkin, L. (1961). Some remarks on infinitely long formulas. Infinitistic Methods. Proceedings Symposium Foundations of Mathematics. Warsaw: Pergamon, pp. 167–183.Google Scholar
Hintikka, J. & Sandu, G. (1989). Informational independence as a semantical phenomenon. In Hilpinen, R., Fenstad, J. E., and Frolov, I. T., editors. Logic, Methodology and Philosophy of Science. Amsterdam: Elsevier, pp. 571–589.Google Scholar
Hodges, W. (1997a). Compositional semantics for a language of imperfect information. Logic Journal of the IGPL, 5, 539–563.Google Scholar
Hodges, W. (1997b). Some strange quantifiers. In Mycielski, J., Rozenberg, G., and Salomaa, A., editors. Structures in Logic and Computer Science: A Selection of Essays in Honor of A. Ehrenfeucht. Lecture Notes in Computer Science, Vol. 1261. London: Springer, pp. 51–65.Google Scholar
Hodges, W. (2001). Formal features of compositionality. Journal of Logic, Language, and Information, 10(1), 7–28.Google Scholar
Hodges, W. (2012). Formalizing the relationship between meaning and syntax. In Hinzen, W., Machery, E., and Werning, M., editors. The Oxford Handbook of Compositionality. Oxford: Oxford University Press, pp. 245–261.Google Scholar
Hodges, W. (2016). Remarks on compositionality. In Abramsky, S., Kontinen, J., Väänänen, J., and Vollmer, H., editors. Dependence Logic: Theory and Applications. Switzerland: Birkhauser, pp. 99–107.Google Scholar
Iemhoff, R. & Yang, F. (2016). Structural completeness in propositional logics of dependence. Archive for Mathematical Logic, 55(7), 955–975.Google Scholar
Janssen, T. (1997). Compositionality. In van Benthem, J. and ter Meulen, A., editors. Handbook of Logic and Language. Amsterdam: Elsevier, pp. 417–473.Google Scholar
Janssen, T. M. V. (1998). Algebraic translations, correctness and algebraic compiler construction. Theoretical Computer Science, 199(1–2), 25–56.Google Scholar
Pagin, P. & Westerståhl, D. (2010). Compositionality I: Definitions and variants. Philosophy Compass, 5, 250–264.CrossRefGoogle Scholar
Peters, S. & Westerståhl, D. (2006). Quantifiers in Language and Logic. Oxford: Clarendon Press.Google Scholar
Rosetta, M. (1994). Compositional Translation. Dordrecht: Kluwer Academic Publishers.Google Scholar
Sano, K. & Virtema, J. (2015). Axiomatizing propositional dependence logics. In Kreutzer, S., editor. Proceedings of the 24th EACSL Annual Conference on Computer Science Logic, Vol. 41. Dagstuhl: Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, pp. 292–307.Google Scholar
Väänänen, J. (2007). Dependence Logic: A New Approach to Independence Friendly Logic. Cambridge: Cambridge University Press.Google Scholar
Yang, F. (2014). On Extensions and Variants of Dependence Logic. Ph.D. thesis, University of Helsinki.Google Scholar
Yang, F. & Väänänen, J. (2016). Propositional logics of dependence. Annals of Pure and Applied Logic, 167(7), 557–589.Google Scholar